Chapter 9.4, Problem 44E

To determine

To calculate the value of $c-d$

Answer to Problem 44E

The value of $c-d$ is 4.

Explanation of Solution

Given information:

  $\begin{array}{l}c+d=12\\ c^2-d^2=48\end{array}$

Calculation:

Write the second equation and expand

  $\begin{array}{l}{c}^2-d^2=48\\ \left(c+d\right)\left(c-d\right)=48\left[a^2-b^2=\left(a+b\right)\left(a-b\right)\right]\\ 12\left(c-d\right)=48\left[c+d=12\right]\\ c-d=4\left[\text{divide each side by 12}\right]\end{array}$

The value of $c-d$ is 4.